Yeah, but you would need a new type certificate if the model of the engine is different from the version that was certified. Not to mention, you'd need a lead-free-compatible engine that physically fits into the plane.

True! But for many popular airframe/engine combinations there are companies which hold supplemental type certificates (STCs) for the conversion, see for instance Petersen Aviation who have a dedicated website for STCs covering conversion to auto fuel: https://www.autofuelstc.com/

I know some enthusiasts have been retrofitting with Subaru boxer engines with some success, but they end up with an X registration.